Blender Crashes Requesting more GPU Memory
You're using a very old graphics card compared to the generations of GPUs being made nowadays. Blender recently increased their system requirements due to all the new features being added. So yeah, its preferable if you get a 4GB or better GPU.

https://www.blender.org/download/requirements/

Edit: A GPU capable of running Blender 2.8 is fairly cheap. You can easily get a Nvidia GTX 1050Ti for somewhere around $140, and it'll be suitable for another 1-2 years before needing a slightly better model to compete with Blender's updates.